The single copy field is the Abelian gauge field \(A_{\mu } = \phi k_{\mu }\) , and \(\phi \)  is the zeroth copy
scalar field. They satisfy the Maxwell equations and the Klein-Gordon wave equation on the flat background \(\eta _{\mu \nu }\) .Much of the double copy
literature uses a flat background owing to its origins in the study of amplitudes in flat spacetime. However, the classical double copy can still be performed in curved spacetimes, and the curved equations of motion can be used; for relevant literature, see [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [7]}, [10]}.
